LMFDB - Embedded newform 43.5.b.b.42.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,5,Mod(42,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.44490841261$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 $ x^12 + 142x^10 + 7173x^8 + 157368x^6 + 1510016x^4 + 5098688*x^2 + 90352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.4
Root			$-3.65497i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.5.b.b.42.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.65497i q^{2} +4.18965i q^{3} +2.64117 q^{4} +45.6695i q^{5} +15.3130 q^{6} +34.3337i q^{7} -68.1330i q^{8} +63.4469 q^{9} +O(q^{10})$	\(q-3.65497i q^{2} +4.18965i q^{3} +2.64117 q^{4} +45.6695i q^{5} +15.3130 q^{6} +34.3337i q^{7} -68.1330i q^{8} +63.4469 q^{9} +166.921 q^{10} -103.099 q^{11} +11.0656i q^{12} +134.875 q^{13} +125.489 q^{14} -191.339 q^{15} -206.765 q^{16} +240.390 q^{17} -231.897i q^{18} -100.800i q^{19} +120.621i q^{20} -143.846 q^{21} +376.825i q^{22} -475.879 q^{23} +285.453 q^{24} -1460.70 q^{25} -492.966i q^{26} +605.181i q^{27} +90.6813i q^{28} -159.825i q^{29} +699.339i q^{30} +1118.26 q^{31} -334.405i q^{32} -431.949i q^{33} -878.620i q^{34} -1568.00 q^{35} +167.574 q^{36} -2451.77i q^{37} -368.423 q^{38} +565.080i q^{39} +3111.60 q^{40} +1069.81 q^{41} +525.754i q^{42} +(1742.01 - 619.833i) q^{43} -272.303 q^{44} +2897.59i q^{45} +1739.32i q^{46} -2933.56 q^{47} -866.274i q^{48} +1222.20 q^{49} +5338.84i q^{50} +1007.15i q^{51} +356.229 q^{52} -825.685 q^{53} +2211.92 q^{54} -4708.49i q^{55} +2339.26 q^{56} +422.318 q^{57} -584.155 q^{58} -1241.46 q^{59} -505.360 q^{60} -6202.15i q^{61} -4087.22i q^{62} +2178.37i q^{63} -4530.49 q^{64} +6159.69i q^{65} -1578.76 q^{66} +265.952 q^{67} +634.912 q^{68} -1993.77i q^{69} +5731.02i q^{70} -3861.16i q^{71} -4322.82i q^{72} +8274.70i q^{73} -8961.14 q^{74} -6119.84i q^{75} -266.231i q^{76} -3539.78i q^{77} +2065.35 q^{78} +4953.26 q^{79} -9442.88i q^{80} +2603.70 q^{81} -3910.14i q^{82} -13512.1 q^{83} -379.923 q^{84} +10978.5i q^{85} +(-2265.47 - 6367.01i) q^{86} +669.609 q^{87} +7024.45i q^{88} +5359.31i q^{89} +10590.6 q^{90} +4630.77i q^{91} -1256.88 q^{92} +4685.12i q^{93} +10722.1i q^{94} +4603.51 q^{95} +1401.04 q^{96} +3191.32 q^{97} -4467.09i q^{98} -6541.32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	3.65497i		−	0.913743i	−0.889533	−	0.456872i	$-0.848970\pi$
$2$		−	3.65497i		−	0.913743i	0.889533	−	0.456872i	$-0.151030\pi$
$3$			4.18965i			0.465516i	0.972535	+	0.232758i	$0.0747751\pi$
$3$			4.18965i			0.465516i	−0.972535	+	0.232758i	$0.925225\pi$
$4$	2.64117			0.165073
$5$			45.6695i			1.82678i	0.407085	+	0.913390i	$0.366545\pi$
$5$			45.6695i			1.82678i	−0.407085	+	0.913390i	$0.633455\pi$
$6$	15.3130			0.425362
$7$			34.3337i			0.700688i	0.936621	+	0.350344i	$0.113935\pi$
$7$			34.3337i			0.700688i	−0.936621	+	0.350344i	$0.886065\pi$
$8$		−	68.1330i		−	1.06458i
$9$	63.4469			0.783295
$10$	166.921			1.66921
$11$	−103.099			−0.852059			−0.426030	−	0.904709i	$-0.640088\pi$
$11$	−103.099			−0.852059			−0.426030	+	0.904709i	$0.640088\pi$
$12$			11.0656i			0.0768443i
$13$	134.875			0.798079			0.399039	−	0.916934i	$-0.369344\pi$
$13$	134.875			0.798079			0.399039	+	0.916934i	$0.369344\pi$
$14$	125.489			0.640249
$15$	−191.339			−0.850396
$16$	−206.765			−0.807678
$17$	240.390			0.831800			0.415900	−	0.909410i	$-0.363467\pi$
$17$	240.390			0.831800			0.415900	+	0.909410i	$0.363467\pi$
$18$		−	231.897i		−	0.715730i
$19$		−	100.800i		−	0.279225i	−0.990206	−	0.139613i	$-0.955414\pi$
$19$		−	100.800i		−	0.279225i	0.990206	−	0.139613i	$-0.0445858\pi$
$20$			120.621i			0.301553i
$21$	−143.846			−0.326182
$22$			376.825i			0.778564i
$23$	−475.879			−0.899582			−0.449791	−	0.893134i	$-0.648502\pi$
$23$	−475.879			−0.899582			−0.449791	+	0.893134i	$0.648502\pi$
$24$	285.453			0.495578
$25$	−1460.70			−2.33713
$26$		−	492.966i		−	0.729239i
$27$			605.181i			0.830153i
$28$			90.6813i			0.115665i
$29$		−	159.825i		−	0.190041i	−0.995475	−	0.0950207i	$-0.969708\pi$
$29$		−	159.825i		−	0.190041i	0.995475	−	0.0950207i	$-0.0302917\pi$
$30$			699.339i			0.777044i
$31$	1118.26			1.16364			0.581822	−	0.813316i	$-0.302340\pi$
$31$	1118.26			1.16364			0.581822	+	0.813316i	$0.302340\pi$
$32$		−	334.405i		−	0.326568i
$33$		−	431.949i		−	0.396648i
$34$		−	878.620i		−	0.760051i
$35$	−1568.00			−1.28000
$36$	167.574			0.129301
$37$		−	2451.77i		−	1.79092i	−0.445145	−	0.895459i	$-0.646848\pi$
$37$		−	2451.77i		−	1.79092i	0.445145	−	0.895459i	$-0.353152\pi$
$38$	−368.423			−0.255140
$39$			565.080i			0.371519i
$40$	3111.60			1.94475
$41$	1069.81			0.636416			0.318208	−	0.948021i	$-0.396919\pi$
$41$	1069.81			0.636416			0.318208	+	0.948021i	$0.396919\pi$
$42$			525.754i			0.298046i
$43$	1742.01	−	619.833i	0.942138	−	0.335226i
$43$	1742.01	−	619.833i	0.942138	−	0.335226i
$44$	−272.303			−0.140652
$45$			2897.59i			1.43091i
$46$			1739.32i			0.821987i
$47$	−2933.56			−1.32800			−0.664002	−	0.747731i	$-0.731143\pi$
$47$	−2933.56			−1.32800			−0.664002	+	0.747731i	$0.731143\pi$
$48$		−	866.274i		−	0.375987i
$49$	1222.20			0.509036
$50$			5338.84i			2.13553i
$51$			1007.15i			0.387216i
$52$	356.229			0.131741
$53$	−825.685			−0.293943			−0.146971	−	0.989141i	$-0.546953\pi$
$53$	−825.685			−0.293943			−0.146971	+	0.989141i	$0.546953\pi$
$54$	2211.92			0.758546
$55$		−	4708.49i		−	1.55653i
$56$	2339.26			0.745937
$57$	422.318			0.129984
$58$	−584.155			−0.173649
$59$	−1241.46			−0.356639			−0.178320	−	0.983973i	$-0.557066\pi$
$59$	−1241.46			−0.356639			−0.178320	+	0.983973i	$0.557066\pi$
$60$	−505.360			−0.140378
$61$		−	6202.15i		−	1.66680i	−0.552673	−	0.833398i	$-0.686392\pi$
$61$		−	6202.15i		−	1.66680i	0.552673	−	0.833398i	$-0.313608\pi$
$62$		−	4087.22i		−	1.06327i
$63$			2178.37i			0.548845i
$64$	−4530.49			−1.10608
$65$			6159.69i			1.45791i
$66$	−1578.76			−0.362434
$67$	265.952			0.0592452			0.0296226	−	0.999561i	$-0.490569\pi$
$67$	265.952			0.0592452			0.0296226	+	0.999561i	$0.490569\pi$
$68$	634.912			0.137308
$69$		−	1993.77i		−	0.418770i
$70$			5731.02i			1.16959i
$71$		−	3861.16i		−	0.765952i	−0.923758	−	0.382976i	$-0.874899\pi$
$71$		−	3861.16i		−	0.765952i	0.923758	−	0.382976i	$-0.125101\pi$
$72$		−	4322.82i		−	0.833878i
$73$			8274.70i			1.55277i	0.630260	+	0.776384i	$0.282948\pi$
$73$			8274.70i			1.55277i	−0.630260	+	0.776384i	$0.717052\pi$
$74$	−8961.14			−1.63644
$75$		−	6119.84i		−	1.08797i
$76$		−	266.231i		−	0.0460926i
$77$		−	3539.78i		−	0.597028i
$78$	2065.35			0.339473
$79$	4953.26			0.793665			0.396833	−	0.917891i	$-0.370109\pi$
$79$	4953.26			0.793665			0.396833	+	0.917891i	$0.370109\pi$
$80$		−	9442.88i		−	1.47545i
$81$	2603.70			0.396845
$82$		−	3910.14i		−	0.581520i
$83$	−13512.1			−1.96140			−0.980700	−	0.195519i	$-0.937361\pi$
$83$	−13512.1			−1.96140			−0.980700	+	0.195519i	$0.937361\pi$
$84$	−379.923			−0.0538439
$85$			10978.5i			1.51952i
$86$	−2265.47	−	6367.01i	−0.306311	−	0.860872i
$87$	669.609			0.0884673
$88$			7024.45i			0.907084i
$89$			5359.31i			0.676595i	0.941039	+	0.338298i	$0.109851\pi$
$89$			5359.31i			0.676595i	−0.941039	+	0.338298i	$0.890149\pi$
$90$	10590.6			1.30748
$91$			4630.77i			0.559204i
$92$	−1256.88			−0.148497
$93$			4685.12i			0.541695i
$94$			10722.1i			1.21345i
$95$	4603.51			0.510084
$96$	1401.04			0.152023
$97$	3191.32			0.339177			0.169588	−	0.985515i	$-0.445756\pi$
$97$	3191.32			0.339177			0.169588	+	0.985515i	$0.445756\pi$
$98$		−	4467.09i		−	0.465128i
$99$	−6541.32			−0.667413
$100$	−3857.97			−0.385797
$101$	6784.27			0.665059			0.332529	−	0.943093i	$-0.392098\pi$
$101$	6784.27			0.665059			0.332529	+	0.943093i	$0.392098\pi$
$102$	3681.11			0.353816
$103$	−650.667			−0.0613316			−0.0306658	−	0.999530i	$-0.509763\pi$
$103$	−650.667			−0.0613316			−0.0306658	+	0.999530i	$0.509763\pi$
$104$		−	9189.46i		−	0.849617i
$105$		−	6569.39i		−	0.595863i
$106$			3017.86i			0.268588i
$107$	15902.5			1.38899			0.694495	−	0.719497i	$-0.255628\pi$
$107$	15902.5			1.38899			0.694495	+	0.719497i	$0.255628\pi$
$108$			1598.39i			0.137036i
$109$	17290.7			1.45533			0.727663	−	0.685935i	$-0.240607\pi$
$109$	17290.7			1.45533			0.727663	+	0.685935i	$0.240607\pi$
$110$	−17209.4			−1.42226
$111$	10272.0			0.833701
$112$		−	7099.03i		−	0.565930i
$113$			15504.7i			1.21425i	0.794607	+	0.607124i	$0.207677\pi$
$113$			15504.7i			1.21425i	−0.794607	+	0.607124i	$0.792323\pi$
$114$		−	1543.56i		−	0.118772i
$115$		−	21733.2i		−	1.64334i
$116$		−	422.125i		−	0.0313707i
$117$	8557.41			0.625131
$118$			4537.51i			0.325877i
$119$			8253.49i			0.582832i
$120$			13036.5i			0.905313i
$121$	−4011.56			−0.273995
$122$	−22668.7			−1.52302
$123$			4482.15i			0.296262i
$124$	2953.52			0.192086
$125$		−	38166.2i		−	2.44264i
$126$	7961.87			0.501504
$127$	−24303.2			−1.50680			−0.753400	−	0.657562i	$-0.771588\pi$
$127$	−24303.2			−1.50680			−0.753400	+	0.657562i	$0.771588\pi$
$128$			11208.3i			0.684102i
$129$	2596.88	+	7298.42i	0.156053	+	0.438581i
$130$	22513.5			1.33216
$131$			6058.45i			0.353036i	0.984297	+	0.176518i	$0.0564834\pi$
$131$			6058.45i			0.353036i	−0.984297	+	0.176518i	$0.943517\pi$
$132$		−	1140.85i		−	0.0654759i
$133$	3460.85			0.195650
$134$		−	972.046i		−	0.0541349i
$135$	−27638.3			−1.51651
$136$		−	16378.5i		−	0.885516i
$137$			20546.4i			1.09470i	0.836905	+	0.547349i	$0.184363\pi$
$137$			20546.4i			1.09470i	−0.836905	+	0.547349i	$0.815637\pi$
$138$	−7287.16			−0.382648
$139$	−7143.71			−0.369738			−0.184869	−	0.982763i	$-0.559186\pi$
$139$	−7143.71			−0.369738			−0.184869	+	0.982763i	$0.559186\pi$
$140$	−4141.37			−0.211294
$141$		−	12290.6i		−	0.618208i
$142$	−14112.4			−0.699883
$143$	−13905.5			−0.680010
$144$	−13118.6			−0.632649
$145$	7299.12			0.347164
$146$	30243.8			1.41883
$147$			5120.57i			0.236965i
$148$		−	6475.54i		−	0.295633i
$149$		−	29115.5i		−	1.31145i	−0.754999	−	0.655726i	$-0.772363\pi$
$149$		−	29115.5i		−	1.31145i	0.754999	−	0.655726i	$-0.227637\pi$
$150$	−22367.8			−0.994126
$151$			11488.6i			0.503864i	0.967745	+	0.251932i	$0.0810659\pi$
$151$			11488.6i			0.503864i	−0.967745	+	0.251932i	$0.918934\pi$
$152$	−6867.83			−0.297257
$153$	15252.0			0.651544
$154$	−12937.8			−0.545530
$155$			51070.5i			2.12572i
$156$			1492.47i			0.0613278i
$157$			2810.63i			0.114026i	0.998373	+	0.0570131i	$0.0181577\pi$
$157$			2810.63i			0.114026i	−0.998373	+	0.0570131i	$0.981842\pi$
$158$		−	18104.0i		−	0.725206i
$159$		−	3459.33i		−	0.136835i
$160$	15272.1			0.596568
$161$		−	16338.7i		−	0.630327i
$162$		−	9516.45i		−	0.362614i
$163$			506.838i			0.0190763i	0.999955	+	0.00953815i	$0.00303613\pi$
$163$			506.838i			0.0190763i	−0.999955	+	0.00953815i	$0.996964\pi$
$164$	2825.56			0.105055
$165$	19726.9			0.724588
$166$			49386.3i			1.79222i
$167$	−45960.0			−1.64796			−0.823980	−	0.566619i	$-0.808251\pi$
$167$	−45960.0			−1.64796			−0.823980	+	0.566619i	$0.808251\pi$
$168$			9800.67i			0.347246i
$169$	−10369.6			−0.363070
$170$	40126.1			1.38845
$171$		−	6395.47i		−	0.218716i
$172$	4600.95	−	1637.09i	0.155522	−	0.0553368i
$173$	−23016.4			−0.769033			−0.384516	−	0.923118i	$-0.625632\pi$
$173$	−23016.4			−0.769033			−0.384516	+	0.923118i	$0.625632\pi$
$174$		−	2447.40i		−	0.0808364i
$175$		−	50151.4i		−	1.63760i
$176$	21317.4			0.688189
$177$		−	5201.28i		−	0.166021i
$178$	19588.1			0.618234
$179$		−	54490.4i		−	1.70065i	−0.526260	−	0.850324i	$-0.676406\pi$
$179$		−	54490.4i		−	1.70065i	0.526260	−	0.850324i	$-0.323594\pi$
$180$			7653.03i			0.236205i
$181$	24427.1			0.745616			0.372808	−	0.927909i	$-0.378395\pi$
$181$	24427.1			0.745616			0.372808	+	0.927909i	$0.378395\pi$
$182$	16925.3			0.510969
$183$	25984.8			0.775921
$184$			32423.1i			0.957675i
$185$	111971.			3.27161
$186$	17124.0			0.494970
$187$	−24784.0			−0.708743
$188$	−7748.04			−0.219218
$189$	−20778.1			−0.581678
$190$		−	16825.7i		−	0.466086i
$191$			25639.4i			0.702815i	0.936223	+	0.351408i	$0.114297\pi$
$191$			25639.4i			0.702815i	−0.936223	+	0.351408i	$0.885703\pi$
$192$		−	18981.2i		−	0.514897i
$193$	−45243.0			−1.21461			−0.607305	−	0.794469i	$-0.707749\pi$
$193$	−45243.0			−1.21461			−0.607305	+	0.794469i	$0.707749\pi$
$194$		−	11664.2i		−	0.309921i
$195$	−25806.9			−0.678683
$196$	3228.03			0.0840282
$197$	−19109.6			−0.492401			−0.246200	−	0.969219i	$-0.579182\pi$
$197$	−19109.6			−0.492401			−0.246200	+	0.969219i	$0.579182\pi$
$198$			23908.3i			0.609845i
$199$			41414.6i			1.04580i	0.852395	+	0.522899i	$0.175149\pi$
$199$			41414.6i			1.04580i	−0.852395	+	0.522899i	$0.824851\pi$
$200$			99522.2i			2.48805i
$201$			1114.24i			0.0275796i
$202$		−	24796.3i		−	0.607693i
$203$	5487.38			0.133160
$204$			2660.06i			0.0639191i
$205$			48857.9i			1.16259i
$206$			2378.17i			0.0560413i
$207$	−30193.0			−0.704638
$208$	−27887.6			−0.644590
$209$			10392.4i			0.237917i
$210$	−24010.9			−0.544466
$211$		−	40579.3i		−	0.911464i	−0.890117	−	0.455732i	$-0.849377\pi$
$211$		−	40579.3i		−	0.911464i	0.890117	−	0.455732i	$-0.150623\pi$
$212$	−2180.78			−0.0485221
$213$	16176.9			0.356563
$214$		−	58123.4i		−	1.26918i
$215$	28307.5	+	79556.9i	0.612384	+	1.72108i
$216$	41232.8			0.883762
$217$			38394.1i			0.815351i
$218$		−	63197.1i		−	1.32979i
$219$	−34668.1			−0.722839
$220$		−	12435.9i		−	0.256941i
$221$	32422.7			0.663842
$222$		−	37544.0i		−	0.761789i
$223$		−	76426.0i		−	1.53685i	−0.639940	−	0.768425i	$-0.721041\pi$
$223$		−	76426.0i		−	1.53685i	0.639940	−	0.768425i	$-0.278959\pi$
$224$	11481.4			0.228822
$225$	−92677.1			−1.83066
$226$	56669.4			1.10951
$227$		−	44850.6i		−	0.870395i	−0.900335	−	0.435197i	$-0.856679\pi$
$227$		−	44850.6i		−	0.870395i	0.900335	−	0.435197i	$-0.143321\pi$
$228$	1115.41			0.0214569
$229$	−68025.3			−1.29718			−0.648589	−	0.761139i	$-0.724640\pi$
$229$	−68025.3			−1.29718			−0.648589	+	0.761139i	$0.724640\pi$
$230$	−79434.1			−1.50159
$231$	14830.4			0.277926
$232$	−10889.3			−0.202314
$233$			61038.6i			1.12433i	0.827026	+	0.562164i	$0.190031\pi$
$233$			61038.6i			1.12433i	−0.827026	+	0.562164i	$0.809969\pi$
$234$		−	31277.1i		−	0.571209i
$235$		−	133974.i		−	2.42597i
$236$	−3278.91			−0.0588716
$237$			20752.4i			0.369464i
$238$	30166.3			0.532559
$239$	−18090.2			−0.316699			−0.158349	−	0.987383i	$-0.550617\pi$
$239$	−18090.2			−0.316699			−0.158349	+	0.987383i	$0.550617\pi$
$240$	39562.3			0.686846
$241$			63866.5i			1.09961i	0.835293	+	0.549805i	$0.185298\pi$
$241$			63866.5i			1.09961i	−0.835293	+	0.549805i	$0.814702\pi$
$242$			14662.1i			0.250361i
$243$			59928.3i			1.01489i
$244$		−	16380.9i		−	0.275144i
$245$			55817.1i			0.929897i
$246$	16382.1			0.270707
$247$		−	13595.5i		−	0.222844i
$248$		−	76190.5i		−	1.23879i
$249$		−	56610.9i		−	0.913064i
$250$	−139497.			−2.23195
$251$	29813.8			0.473227			0.236613	−	0.971604i	$-0.423963\pi$
$251$	29813.8			0.473227			0.236613	+	0.971604i	$0.423963\pi$
$252$			5753.44i			0.0905997i
$253$	49062.7			0.766497
$254$			88827.5i			1.37683i
$255$	−45996.0			−0.707359
$256$	−31521.7			−0.480983
$257$		−	56144.1i		−	0.850037i	−0.905185	−	0.425018i	$-0.860268\pi$
$257$		−	56144.1i		−	0.850037i	0.905185	−	0.425018i	$-0.139732\pi$
$258$	26675.5	−	9491.53i	0.400750	−	0.142593i
$259$	84178.3			1.25487
$260$			16268.8i			0.240663i
$261$		−	10140.4i		−	0.148858i
$262$	22143.5			0.322584
$263$			7995.51i			0.115594i	0.998328	+	0.0577969i	$0.0184076\pi$
$263$			7995.51i			0.115594i	−0.998328	+	0.0577969i	$0.981592\pi$
$264$	−29430.0			−0.422262
$265$		−	37708.6i		−	0.536969i
$266$		−	12649.3i		−	0.178774i
$267$	−22453.6			−0.314966
$268$	702.424			0.00977980
$269$	6211.47			0.0858401			0.0429200	−	0.999079i	$-0.486334\pi$
$269$	6211.47			0.0858401			0.0429200	+	0.999079i	$0.486334\pi$
$270$			101017.i			1.38570i
$271$	−15284.9			−0.208125			−0.104063	−	0.994571i	$-0.533184\pi$
$271$	−15284.9			−0.208125			−0.104063	+	0.994571i	$0.533184\pi$
$272$	−49704.4			−0.671826
$273$	−19401.3			−0.260319
$274$	75096.4			1.00027
$275$	150597.			1.99137
$276$		−	5265.88i		−	0.0691278i
$277$			44696.5i			0.582525i	0.956643	+	0.291262i	$0.0940753\pi$
$277$			44696.5i			0.582525i	−0.956643	+	0.291262i	$0.905925\pi$
$278$			26110.1i			0.337846i
$279$	70950.2			0.911476
$280$			106833.i			1.36266i
$281$	91345.4			1.15684			0.578421	−	0.815739i	$-0.303669\pi$
$281$	91345.4			1.15684			0.578421	+	0.815739i	$0.303669\pi$
$282$	−44921.8			−0.564883
$283$	25305.7			0.315970			0.157985	−	0.987442i	$-0.449500\pi$
$283$	25305.7			0.315970			0.157985	+	0.987442i	$0.449500\pi$
$284$		−	10198.0i		−	0.126438i
$285$			19287.1i			0.237452i
$286$			50824.4i			0.621355i
$287$			36730.7i			0.445929i
$288$		−	21217.0i		−	0.255799i
$289$	−25733.6			−0.308109
$290$		−	26678.1i		−	0.317219i
$291$			13370.5i			0.157892i
$292$			21854.9i			0.256320i
$293$	5876.11			0.0684470			0.0342235	−	0.999414i	$-0.489104\pi$
$293$	5876.11			0.0684470			0.0342235	+	0.999414i	$0.489104\pi$
$294$	18715.5			0.216525
$295$		−	56696.9i		−	0.651501i
$296$	−167046.			−1.90657
$297$		−	62393.7i		−	0.707339i
$298$	−106417.			−1.19833
$299$	−64184.3			−0.717938
$300$		−	16163.5i		−	0.179595i
$301$	21281.2	+	59809.8i	0.234889	+	0.660145i
$302$	41990.5			0.460402
$303$			28423.7i			0.309596i
$304$			20842.0i			0.225524i
$305$	283249.			3.04487
$306$		−	55745.6i		−	0.595344i
$307$	−82720.6			−0.877681			−0.438841	−	0.898565i	$-0.644611\pi$
$307$	−82720.6			−0.877681			−0.438841	+	0.898565i	$0.644611\pi$
$308$		−	9349.16i		−	0.0985533i
$309$		−	2726.07i		−	0.0285509i
$310$	186661.			1.94236
$311$	160383.			1.65820			0.829102	−	0.559097i	$-0.188852\pi$
$311$	160383.			1.65820			0.829102	+	0.559097i	$0.188852\pi$
$312$	38500.6			0.395511
$313$		−	182768.i		−	1.86557i	−0.360429	−	0.932787i	$-0.617370\pi$
$313$		−	182768.i		−	1.86557i	0.360429	−	0.932787i	$-0.382630\pi$
$314$	10272.8			0.104191
$315$	−99485.0			−1.00262
$316$	13082.4			0.131013
$317$	−99340.5			−0.988571			−0.494286	−	0.869300i	$-0.664570\pi$
$317$	−99340.5			−0.988571			−0.494286	+	0.869300i	$0.664570\pi$
$318$	−12643.8			−0.125032
$319$			16477.8i			0.161926i
$320$		−	206905.i		−	2.02056i
$321$			66626.1i			0.646598i
$322$	−59717.5			−0.575957
$323$		−	24231.4i		−	0.232260i
$324$	6876.82			0.0655085
$325$	−197013.			−1.86521
$326$	1852.48			0.0174308
$327$			72442.0i			0.677478i
$328$		−	72889.7i		−	0.677514i
$329$		−	100720.i		−	0.930517i
$330$		−	72101.3i		−	0.662088i
$331$			128433.i			1.17225i	0.810221	+	0.586124i	$0.199347\pi$
$331$			128433.i			1.17225i	−0.810221	+	0.586124i	$0.800653\pi$
$332$	−35687.7			−0.323775
$333$		−	155557.i		−	1.40282i
$334$			167982.i			1.50581i
$335$			12145.9i			0.108228i
$336$	29742.4			0.263450
$337$	−78727.5			−0.693213			−0.346606	−	0.938011i	$-0.612666\pi$
$337$	−78727.5			−0.693213			−0.346606	+	0.938011i	$0.612666\pi$
$338$			37900.8i			0.331753i
$339$	−64959.4			−0.565252
$340$			28996.1i			0.250831i
$341$	−115292.			−0.991493
$342$	−23375.3			−0.199850
$343$			124398.i			1.05736i
$344$	−42231.1	−	118689.i	−0.356874	−	1.00298i
$345$	91054.3			0.765001
$346$			84124.3i			0.702699i
$347$			136310.i			1.13205i	0.824387	+	0.566027i	$0.191520\pi$
$347$			136310.i			1.13205i	−0.824387	+	0.566027i	$0.808480\pi$
$348$	1768.55			0.0146036
$349$			48465.9i			0.397910i	0.980009	+	0.198955i	$0.0637548\pi$
$349$			48465.9i			0.397910i	−0.980009	+	0.198955i	$0.936245\pi$
$350$	−183302.			−1.49634
$351$			81624.0i			0.662527i
$352$			34476.9i			0.278255i
$353$	25854.2			0.207483			0.103741	−	0.994604i	$-0.466919\pi$
$353$	25854.2			0.207483			0.103741	+	0.994604i	$0.466919\pi$
$354$	−19010.5			−0.151701
$355$	176337.			1.39923
$356$			14154.9i			0.111688i
$357$	−34579.2			−0.271318
$358$	−199161.			−1.55395
$359$	−125163.			−0.971155			−0.485577	−	0.874194i	$-0.661391\pi$
$359$	−125163.			−0.971155			−0.485577	+	0.874194i	$0.661391\pi$
$360$	197421.			1.52331
$361$	120160.			0.922033
$362$		−	89280.5i		−	0.681301i
$363$		−	16807.0i		−	0.127549i
$364$			12230.7i			0.0923097i
$365$	−377901.			−2.83657
$366$		−	94973.8i		−	0.708993i
$367$	112207.			0.833082			0.416541	−	0.909117i	$-0.363242\pi$
$367$	112207.			0.833082			0.416541	+	0.909117i	$0.363242\pi$
$368$	98395.3			0.726572
$369$	67876.4			0.498501
$370$		−	409251.i		−	2.98941i
$371$		−	28348.9i		−	0.205962i
$372$			12374.2i			0.0894194i
$373$			35635.8i			0.256135i	0.991765	+	0.128068i	$0.0408775\pi$
$373$			35635.8i			0.256135i	−0.991765	+	0.128068i	$0.959123\pi$
$374$			90585.0i			0.647609i
$375$	159903.			1.13709
$376$			199872.i			1.41376i
$377$		−	21556.4i		−	0.151668i
$378$			75943.5i			0.531505i
$379$	−205315.			−1.42936			−0.714679	−	0.699452i	$-0.753427\pi$
$379$	−205315.			−1.42936			−0.714679	+	0.699452i	$0.753427\pi$
$380$	12158.6			0.0842012
$381$		−	101822.i		−	0.701440i
$382$	93711.3			0.642193
$383$		−	164110.i		−	1.11876i	−0.828912	−	0.559380i	$-0.811039\pi$
$383$		−	164110.i		−	1.11876i	0.828912	−	0.559380i	$-0.188961\pi$
$384$	−46959.0			−0.318461
$385$	161660.			1.09064
$386$			165362.i			1.10984i
$387$	110525.	−	39326.5i	0.737971	−	0.262581i
$388$	8428.81			0.0559890
$389$		−	190984.i		−	1.26211i	−0.775738	−	0.631055i	$-0.782622\pi$
$389$		−	190984.i		−	1.26211i	0.775738	−	0.631055i	$-0.217378\pi$
$390$			94323.6i			0.620142i
$391$	−114397.			−0.748272
$392$		−	83271.8i		−	0.541908i
$393$	−25382.8			−0.164344
$394$			69845.0i			0.449928i
$395$			226213.i			1.44985i
$396$	−17276.7			−0.110172
$397$	−170575.			−1.08226			−0.541132	−	0.840938i	$-0.682004\pi$
$397$	−170575.			−1.08226			−0.541132	+	0.840938i	$0.682004\pi$
$398$	151369.			0.955590
$399$			14499.8i			0.0910783i
$400$	302023.			1.88765
$401$	52348.9			0.325551			0.162775	−	0.986663i	$-0.447955\pi$
$401$	52348.9			0.325551			0.162775	+	0.986663i	$0.447955\pi$
$402$	4072.53			0.0252007
$403$	150826.			0.928679
$404$	17918.4			0.109783
$405$			118910.i			0.724949i
$406$		−	20056.2i		−	0.121674i
$407$			252775.i			1.52597i
$408$	68620.1			0.412222
$409$			164844.i			0.985430i	0.870191	+	0.492715i	$0.163996\pi$
$409$			164844.i			0.985430i	−0.870191	+	0.492715i	$0.836004\pi$
$410$	178574.			1.06231
$411$	−86082.0			−0.509599
$412$	−1718.52			−0.0101242
$413$		−	42624.0i		−	0.249893i
$414$			110355.i			0.643858i
$415$		−	617090.i		−	3.58305i
$416$		−	45103.0i		−	0.260627i
$417$		−	29929.6i		−	0.172119i
$418$	37984.1			0.217395
$419$		−	37268.6i		−	0.212283i	−0.994351	−	0.106141i	$-0.966150\pi$
$419$		−	37268.6i		−	0.212283i	0.994351	−	0.106141i	$-0.0338496\pi$
$420$		−	17350.9i		−	0.0983610i
$421$			99646.0i			0.562206i	0.959678	+	0.281103i	$0.0907003\pi$
$421$			99646.0i			0.562206i	−0.959678	+	0.281103i	$0.909300\pi$
$422$	−148316.			−0.832844
$423$	−186125.			−1.04022
$424$			56256.4i			0.312925i
$425$	−351139.			−1.94402
$426$		−	59126.2i		−	0.325807i
$427$	212943.			1.16790
$428$	42001.4			0.229285
$429$		−	58259.3i		−	0.316556i
$430$	290778.	−	103463.i	1.57262	−	0.559562i
$431$	144175.			0.776133			0.388067	−	0.921631i	$-0.373143\pi$
$431$	144175.			0.776133			0.388067	+	0.921631i	$0.373143\pi$
$432$		−	125131.i		−	0.670496i
$433$			220583.i			1.17651i	0.808675	+	0.588256i	$0.200185\pi$
$433$			220583.i			1.17651i	−0.808675	+	0.588256i	$0.799815\pi$
$434$	140329.			0.745022
$435$			30580.7i			0.161610i
$436$	45667.8			0.240235
$437$			47968.8i			0.251186i
$438$			126711.i			0.660489i
$439$	68794.6			0.356965			0.178482	−	0.983943i	$-0.442881\pi$
$439$	68794.6			0.356965			0.178482	+	0.983943i	$0.442881\pi$
$440$	−320803.			−1.65704
$441$	77544.4			0.398725
$442$		−	118504.i		−	0.606581i
$443$	321595.			1.63871			0.819355	−	0.573286i	$-0.194332\pi$
$443$	321595.			1.63871			0.819355	+	0.573286i	$0.194332\pi$
$444$	27130.2			0.137622
$445$	−244757.			−1.23599
$446$	−279335.			−1.40429
$447$	121984.			0.610502
$448$		−	155549.i		−	0.775015i
$449$		−	2687.03i		−	0.0133285i	−0.999978	−	0.00666423i	$-0.997879\pi$
$449$		−	2687.03i		−	0.0133285i	0.999978	−	0.00666423i	$-0.00212131\pi$
$450$			338732.i			1.67275i
$451$	−110297.			−0.542264
$452$			40950.7i			0.200440i
$453$	−48133.2			−0.234557
$454$	−163928.			−0.795318
$455$	−211485.			−1.02154
$456$		−	28773.8i		−	0.138378i
$457$		−	222198.i		−	1.06392i	−0.846770	−	0.531959i	$-0.821456\pi$
$457$		−	222198.i		−	1.06392i	0.846770	−	0.531959i	$-0.178544\pi$
$458$			248631.i			1.18529i
$459$			145480.i			0.690521i
$460$		−	57401.0i		−	0.271271i
$461$	−63915.9			−0.300751			−0.150375	−	0.988629i	$-0.548048\pi$
$461$	−63915.9			−0.300751			−0.150375	+	0.988629i	$0.548048\pi$
$462$		−	54204.8i		−	0.253953i
$463$			94323.6i			0.440006i	0.975499	+	0.220003i	$0.0706067\pi$
$463$			94323.6i			0.440006i	−0.975499	+	0.220003i	$0.929393\pi$
$464$			33046.2i			0.153492i
$465$	−213967.			−0.989558
$466$	223094.			1.02735
$467$		−	288915.i		−	1.32476i	−0.749170	−	0.662378i	$-0.769547\pi$
$467$		−	288915.i		−	1.32476i	0.749170	−	0.662378i	$-0.230453\pi$
$468$	22601.6			0.103192
$469$			9131.11i			0.0415124i
$470$	−489673.			−2.21672
$471$	−11775.5			−0.0530810
$472$			84584.4i			0.379670i
$473$	−179600.	+	63904.3i	−0.802757	+	0.285632i
$474$	75849.6			0.337595
$475$			147240.i			0.652586i
$476$			21798.9i			0.0962100i
$477$	−52387.1			−0.230244
$478$			66119.0i			0.289381i
$479$	328139.			1.43017			0.715084	−	0.699039i	$-0.246388\pi$
$479$	328139.			1.43017			0.715084	+	0.699039i	$0.246388\pi$
$480$			63984.9i			0.277712i
$481$		−	330683.i		−	1.42929i
$482$	233430.			1.00476
$483$	68453.4			0.293427
$484$	−10595.2			−0.0452292
$485$			145746.i			0.619602i
$486$	219036.			0.927349
$487$	−225179.			−0.949447			−0.474723	−	0.880135i	$-0.657452\pi$
$487$	−225179.			−0.949447			−0.474723	+	0.880135i	$0.657452\pi$
$488$	−422571.			−1.77443
$489$	−2123.47			−0.00888033
$490$	204010.			0.849687
$491$		−	119348.i		−	0.495053i	−0.968881	−	0.247526i	$-0.920382\pi$
$491$		−	119348.i		−	0.495053i	0.968881	−	0.247526i	$-0.0796177\pi$
$492$			11838.1i			0.0489049i
$493$		−	38420.3i		−	0.158076i
$494$	−49691.1			−0.203622
$495$		−	298739.i		−	1.21922i
$496$	−231218.			−0.939849
$497$	132568.			0.536693
$498$	−206911.			−0.834306
$499$		−	184960.i		−	0.742807i	−0.928471	−	0.371404i	$-0.878877\pi$
$499$		−	184960.i		−	0.742807i	0.928471	−	0.371404i	$-0.121123\pi$
$500$		−	100804.i		−	0.403214i
$501$		−	192556.i		−	0.767153i
$502$		−	108968.i		−	0.432408i
$503$		−	340779.i		−	1.34691i	−0.739230	−	0.673453i	$-0.764810\pi$
$503$		−	340779.i		−	1.34691i	0.739230	−	0.673453i	$-0.235190\pi$
$504$	148419.			0.584289
$505$			309834.i			1.21492i
$506$		−	179323.i		−	0.700382i
$507$		−	43445.2i		−	0.169015i
$508$	−64188.9			−0.248732
$509$	35186.6			0.135813			0.0679066	−	0.997692i	$-0.478368\pi$
$509$	35186.6			0.135813			0.0679066	+	0.997692i	$0.478368\pi$
$510$			168114.i			0.646345i
$511$	−284101.			−1.08801
$512$			294544.i			1.12360i
$513$	61002.5			0.231800
$514$	−205205.			−0.776715
$515$		−	29715.7i		−	0.112039i
$516$	6858.81	+	19276.4i	0.0257602	+	0.0723979i
$517$	302448.			1.13154
$518$		−	307669.i		−	1.14663i
$519$		−	96430.5i		−	0.357997i
$520$	419678.			1.55206
$521$		−	167672.i		−	0.617712i	−0.951109	−	0.308856i	$-0.900054\pi$
$521$		−	167672.i		−	0.617712i	0.951109	−	0.308856i	$-0.0999460\pi$
$522$	−37062.8			−0.136018
$523$			388697.i			1.42105i	0.703674	+	0.710523i	$0.251541\pi$
$523$			388697.i			1.42105i	−0.703674	+	0.710523i	$0.748459\pi$
$524$			16001.4i			0.0582768i
$525$	210117.			0.762329
$526$	29223.4			0.105623
$527$	268819.			0.967918
$528$			89312.2i			0.320363i
$529$	−53380.2			−0.190752
$530$	−137824.			−0.490652
$531$	−78766.8			−0.279353
$532$	9140.71			0.0322966
$533$	144292.			0.507910
$534$			82067.4i			0.287798i
$535$			726262.i			2.53738i
$536$		−	18120.1i		−	0.0630711i
$537$	228296.			0.791679
$538$		−	22702.8i		−	0.0784358i
$539$	−126007.			−0.433729
$540$	−72997.6			−0.250335
$541$	258688.			0.883856			0.441928	−	0.897050i	$-0.354295\pi$
$541$	258688.			0.883856			0.441928	+	0.897050i	$0.354295\pi$
$542$			55865.9i			0.190173i
$543$			102341.i			0.347096i
$544$		−	80387.8i		−	0.271639i
$545$			789659.i			2.65856i
$546$			70911.2i			0.237865i
$547$	−11333.8			−0.0378791			−0.0189395	−	0.999821i	$-0.506029\pi$
$547$	−11333.8			−0.0378791			−0.0189395	+	0.999821i	$0.506029\pi$
$548$			54266.5i			0.180705i
$549$		−	393507.i		−	1.30559i
$550$		−	550430.i		−	1.81960i
$551$	−16110.4			−0.0530644
$552$	−135841.			−0.445814
$553$			170064.i			0.556112i
$554$	163365.			0.532278
$555$			469119.i			1.52299i
$556$	−18867.8			−0.0610338
$557$	−90762.0			−0.292546			−0.146273	−	0.989244i	$-0.546728\pi$
$557$	−90762.0			−0.292546			−0.146273	+	0.989244i	$0.546728\pi$
$558$		−	259321.i		−	0.832855i
$559$	234955.	−	83600.2i	0.751900	−	0.267537i
$560$	324209.			1.03383
$561$		−	103836.i		−	0.329931i
$562$		−	333865.i		−	1.05706i
$563$	198527.			0.626329			0.313165	−	0.949699i	$-0.398611\pi$
$563$	198527.			0.626329			0.313165	+	0.949699i	$0.398611\pi$
$564$		−	32461.5i		−	0.102050i
$565$	−708094.			−2.21817
$566$		−	92491.8i		−	0.288716i
$567$			89394.7i			0.278065i
$568$	−263073.			−0.815415
$569$	204563.			0.631832			0.315916	−	0.948787i	$-0.397688\pi$
$569$	204563.			0.631832			0.315916	+	0.948787i	$0.397688\pi$
$570$	70493.7			0.216970
$571$			103248.i			0.316670i	0.987385	+	0.158335i	$0.0506127\pi$
$571$			103248.i			0.316670i	−0.987385	+	0.158335i	$0.949387\pi$
$572$	−36726.9			−0.112252
$573$	−107420.			−0.327172
$574$	134250.			0.407465
$575$	695119.			2.10244
$576$	−287445.			−0.866384
$577$			214909.i			0.645510i	0.946482	+	0.322755i	$0.104609\pi$
$577$			214909.i			0.645510i	−0.946482	+	0.322755i	$0.895391\pi$
$578$			94055.5i			0.281533i
$579$		−	189552.i		−	0.565421i
$580$	19278.2			0.0573075
$581$		−	463920.i		−	1.37433i
$582$	48868.8			0.144273
$583$	85127.5			0.250457
$584$	563780.			1.65304
$585$			390813.i			1.14198i
$586$		−	21477.0i		−	0.0625430i
$587$			508043.i			1.47443i	0.675657	+	0.737216i	$0.263860\pi$
$587$			508043.i			1.47443i	−0.675657	+	0.737216i	$0.736140\pi$
$588$			13524.3i			0.0391165i
$589$		−	112721.i		−	0.324919i
$590$	−207226.			−0.595305
$591$		−	80062.4i		−	0.229221i
$592$			506941.i			1.44648i
$593$			182995.i			0.520390i	0.965556	+	0.260195i	$0.0837869\pi$
$593$			182995.i			0.520390i	−0.965556	+	0.260195i	$0.916213\pi$
$594$	−228047.			−0.646327
$595$	−376933.			−1.06471
$596$		−	76899.1i		−	0.216486i
$597$	−173513.			−0.486836
$598$			234592.i			0.656011i
$599$	−173564.			−0.483733			−0.241867	−	0.970310i	$-0.577760\pi$
$599$	−173564.			−0.483733			−0.241867	+	0.970310i	$0.577760\pi$
$600$	−416963.			−1.15823
$601$		−	370900.i		−	1.02685i	−0.858134	−	0.513426i	$-0.828376\pi$
$601$		−	370900.i		−	1.02685i	0.858134	−	0.513426i	$-0.171624\pi$
$602$	218603.	−	77782.1i	0.603203	−	0.214628i
$603$	16873.8			0.0464064
$604$			30343.4i			0.0831744i
$605$		−	183206.i		−	0.500529i
$606$	103888.			0.282891
$607$			274917.i			0.746147i	0.927802	+	0.373074i	$0.121696\pi$
$607$			274917.i			0.746147i	−0.927802	+	0.373074i	$0.878304\pi$
$608$	−33708.2			−0.0911861
$609$			22990.2i			0.0619880i
$610$		−	1.03527e6i		−	2.78223i
$611$	−395665.			−1.05985
$612$	40283.2			0.107553
$613$	358829.			0.954919			0.477459	−	0.878654i	$-0.341558\pi$
$613$	358829.			0.954919			0.477459	+	0.878654i	$0.341558\pi$
$614$			302342.i			0.801975i
$615$	−204697.			−0.541205
$616$	−241176.			−0.635583
$617$	275204.			0.722909			0.361455	−	0.932390i	$-0.382280\pi$
$617$	275204.			0.722909			0.361455	+	0.932390i	$0.382280\pi$
$618$	−9963.70			−0.0260882
$619$	−303567.			−0.792270			−0.396135	−	0.918192i	$-0.629649\pi$
$619$	−303567.			−0.792270			−0.396135	+	0.918192i	$0.629649\pi$
$620$			134886.i			0.350900i
$621$		−	287993.i		−	0.746791i
$622$		−	586196.i		−	1.51517i
$623$	−184005.			−0.474082
$624$		−	116839.i		−	0.300067i
$625$	830093.			2.12504
$626$	−668013.			−1.70466
$627$	−43540.6			−0.110754
$628$			7423.36i			0.0188227i
$629$		−	589380.i		−	1.48968i
$630$			363615.i			0.916137i
$631$		−	350000.i		−	0.879041i	−0.898233	−	0.439520i	$-0.855148\pi$
$631$		−	350000.i		−	0.879041i	0.898233	−	0.439520i	$-0.144852\pi$
$632$		−	337481.i		−	0.844918i
$633$	170013.			0.424302
$634$			363087.i			0.903300i
$635$		−	1.10991e6i		−	2.75259i
$636$		−	9136.68i		−	0.0225878i
$637$	164844.			0.406251
$638$	60225.9			0.147959
$639$		−	244979.i		−	0.599966i
$640$	−511879.			−1.24970
$641$			404169.i			0.983665i	0.870690	+	0.491832i	$0.163673\pi$
$641$			404169.i			0.983665i	−0.870690	+	0.491832i	$0.836327\pi$
$642$	243516.			0.590824
$643$	488598.			1.18176			0.590881	−	0.806759i	$-0.298780\pi$
$643$	488598.			1.18176			0.590881	+	0.806759i	$0.298780\pi$
$644$		−	43153.3i		−	0.104050i
$645$	−333315.	+	118598.i	−0.801190	+	0.285075i
$646$	−88565.2			−0.212226
$647$			111849.i			0.267191i	0.991036	+	0.133595i	$0.0426523\pi$
$647$			111849.i			0.267191i	−0.991036	+	0.133595i	$0.957348\pi$
$648$		−	177398.i		−	0.422472i
$649$	127994.			0.303878
$650$			720077.i			1.70433i
$651$	−160858.			−0.379559
$652$			1338.65i			0.00314899i
$653$			92008.4i			0.215775i	0.994163	+	0.107887i	$0.0344086\pi$
$653$			92008.4i			0.215775i	−0.994163	+	0.107887i	$0.965591\pi$
$654$	264774.			0.619041
$655$	−276686.			−0.644919
$656$	−221201.			−0.514019
$657$			525004.i			1.21627i
$658$	−368129.			−0.850254
$659$	−532415.			−1.22597			−0.612985	−	0.790095i	$-0.710031\pi$
$659$	−532415.			−1.22597			−0.612985	+	0.790095i	$0.710031\pi$
$660$	52102.2			0.119610
$661$	−770144.			−1.76266			−0.881331	−	0.472499i	$-0.843352\pi$
$661$	−770144.			−1.76266			−0.881331	+	0.472499i	$0.843352\pi$
$662$	469418.			1.07113
$663$			135840.i			0.309029i
$664$			920618.i			2.08806i
$665$			158055.i			0.357410i
$666$	−568556.			−1.28181
$667$			76057.3i			0.170958i
$668$	−121388.			−0.272034
$669$	320198.			0.715429
$670$	44392.9			0.0988926
$671$			639437.i			1.42021i
$672$			48103.0i			0.106521i
$673$		−	296438.i		−	0.654492i	−0.944939	−	0.327246i	$-0.893879\pi$
$673$		−	296438.i		−	0.654492i	0.944939	−	0.327246i	$-0.106121\pi$
$674$			287747.i			0.633418i
$675$		−	883991.i		−	1.94017i
$676$	−27388.0			−0.0599332
$677$			255234.i			0.556880i	0.960454	+	0.278440i	$0.0898174\pi$
$677$			255234.i			0.556880i	−0.960454	+	0.278440i	$0.910183\pi$
$678$			237425.i			0.516496i
$679$			109570.i			0.237657i
$680$	747998.			1.61764
$681$	187908.			0.405183
$682$			421389.i			0.905970i
$683$	659236.			1.41319			0.706594	−	0.707620i	$-0.250231\pi$
$683$	659236.			1.41319			0.706594	+	0.707620i	$0.250231\pi$
$684$		−	16891.5i		−	0.0361041i
$685$	−938343.			−1.99977
$686$	454671.			0.966159
$687$		−	285002.i		−	0.603857i
$688$	−360188.	+	128160.i	−0.760944	+	0.270755i
$689$	−111365.			−0.234589
$690$		−	332801.i		−	0.699015i
$691$			428774.i			0.897993i	0.893534	+	0.448996i	$0.148218\pi$
$691$			428774.i			0.897993i	−0.893534	+	0.448996i	$0.851782\pi$
$692$	−60790.2			−0.126947
$693$		−	224588.i		−	0.467649i
$694$	498208.			1.03441
$695$		−	326250.i		−	0.675430i
$696$		−	45622.5i		−	0.0941804i
$697$	257173.			0.529370
$698$	177141.			0.363588
$699$	−255730.			−0.523393
$700$		−	132459.i		−	0.270324i
$701$	446529.			0.908686			0.454343	−	0.890827i	$-0.349874\pi$
$701$	446529.			0.908686			0.454343	+	0.890827i	$0.349874\pi$
$702$	298334.			0.605380
$703$	−247139.			−0.500070
$704$	467090.			0.942443
$705$	561305.			1.12933
$706$		−	94496.5i		−	0.189586i
$707$			232929.i			0.465999i
$708$		−	13737.5i		−	0.0274057i
$709$	−43598.6			−0.0867321			−0.0433660	−	0.999059i	$-0.513808\pi$
$709$	−43598.6			−0.0867321			−0.0433660	+	0.999059i	$0.513808\pi$
$710$		−	644509.i		−	1.27853i
$711$	314269.			0.621673
$712$	365146.			0.720288
$713$	−532157.			−1.04679
$714$			126386.i			0.247915i
$715$		−	635059.i		−	1.24223i
$716$		−	143919.i		−	0.280731i
$717$		−	75791.4i		−	0.147429i
$718$			457469.i			0.887386i
$719$	46047.8			0.0890741			0.0445370	−	0.999008i	$-0.485819\pi$
$719$	46047.8			0.0890741			0.0445370	+	0.999008i	$0.485819\pi$
$720$		−	599121.i		−	1.15571i
$721$		−	22339.8i		−	0.0429743i
$722$		−	439183.i		−	0.842502i
$723$	−267578.			−0.511887
$724$	64516.2			0.123081
$725$			233457.i			0.444151i
$726$	−61429.2			−0.116547
$727$		−	275601.i		−	0.521450i	−0.965413	−	0.260725i	$-0.916038\pi$
$727$		−	275601.i		−	0.521450i	0.965413	−	0.260725i	$-0.0839615\pi$
$728$	315508.			0.595317
$729$	−40178.7			−0.0756032
$730$			1.38122e6i			2.59189i
$731$	418763.	−	149002.i	0.783670	−	0.278841i
$732$	68630.4			0.128084
$733$			324631.i			0.604201i	0.953276	+	0.302101i	$0.0976879\pi$
$733$			324631.i			0.604201i	−0.953276	+	0.302101i	$0.902312\pi$
$734$		−	410114.i		−	0.761223i
$735$	−233854.			−0.432882
$736$			159137.i			0.293775i
$737$	−27419.4			−0.0504804
$738$		−	248086.i		−	0.455502i
$739$			359031.i			0.657421i	0.944431	+	0.328710i	$0.106614\pi$
$739$			359031.i			0.657421i	−0.944431	+	0.328710i	$0.893386\pi$
$740$	295735.			0.540056
$741$	56960.3			0.103737
$742$	−103614.			−0.188197
$743$			164101.i			0.297259i	0.988893	+	0.148629i	$0.0474862\pi$
$743$			164101.i			0.297259i	−0.988893	+	0.148629i	$0.952514\pi$
$744$	319211.			0.576677
$745$	1.32969e6			2.39573
$746$	130248.			0.234042
$747$	−857299.			−1.53635
$748$	−65458.9			−0.116994
$749$			545994.i			0.973249i
$750$		−	584441.i		−	1.03901i
$751$		−	862173.i		−	1.52867i	−0.644818	−	0.764336i	$-0.723067\pi$
$751$		−	862173.i		−	1.52867i	0.644818	−	0.764336i	$-0.276933\pi$
$752$	606559.			1.07260
$753$			124909.i			0.220295i
$754$	−78788.1			−0.138586
$755$	−524679.			−0.920449
$756$	−54878.6			−0.0960195
$757$		−	878771.i		−	1.53350i	−0.641946	−	0.766750i	$-0.721873\pi$
$757$		−	878771.i		−	1.53350i	0.641946	−	0.766750i	$-0.278127\pi$
$758$			750419.i			1.30607i
$759$			205556.i			0.356817i
$760$		−	313651.i		−	0.543024i
$761$			452736.i			0.781763i	0.920441	+	0.390882i	$0.127830\pi$
$761$			452736.i			0.781763i	−0.920441	+	0.390882i	$0.872170\pi$
$762$	−372156.			−0.640936
$763$			593655.i			1.01973i
$764$			67718.1i			0.116016i
$765$			696551.i			1.19023i
$766$	−599816.			−1.02226
$767$	−167442.			−0.284626
$768$		−	132065.i		−	0.223905i
$769$	379858.			0.642346			0.321173	−	0.947021i	$-0.395923\pi$
$769$	379858.			0.642346			0.321173	+	0.947021i	$0.395923\pi$
$770$		−	590863.i		−	0.996564i
$771$	235224.			0.395706
$772$	−119495.			−0.200500
$773$		−	466697.i		−	0.781044i	−0.920594	−	0.390522i	$-0.872295\pi$
$773$		−	466697.i		−	0.781044i	0.920594	−	0.390522i	$-0.127705\pi$
$774$	−143737.	−	403967.i	−0.239931	−	0.674316i
$775$	−1.63345e6			−2.71958
$776$		−	217434.i		−	0.361080i
$777$			352677.i			0.584165i
$778$	−698041.			−1.15325
$779$		−	107838.i		−	0.177703i
$780$	−68160.5			−0.112032
$781$			398083.i			0.652636i
$782$			418117.i			0.683729i
$783$	96723.0			0.157763
$784$	−252708.			−0.411137
$785$	−128360.			−0.208301
$786$			92773.3i			0.150168i
$787$	946342.			1.52791			0.763956	−	0.645268i	$-0.223254\pi$
$787$	946342.			1.52791			0.763956	+	0.645268i	$0.223254\pi$
$788$	−50471.7			−0.0812822
$789$	−33498.3			−0.0538108
$790$	826803.			1.32479
$791$	−532335.			−0.850810
$792$			445680.i			0.710514i
$793$		−	836517.i		−	1.33024i
$794$			623446.i			0.988912i
$795$	157986.			0.249968
$796$			109383.i			0.172633i
$797$	−561047.			−0.883248			−0.441624	−	0.897200i	$-0.645597\pi$
$797$	−561047.			−0.883248			−0.441624	+	0.897200i	$0.645597\pi$
$798$	52996.2			0.0832222
$799$	−705199.			−1.10463
$800$			488468.i			0.763231i
$801$			340031.i			0.529973i
$802$		−	191334.i		−	0.297470i
$803$		−	853115.i		−	1.32305i
$804$			2942.91i			0.00455266i
$805$	746181.			1.15147
$806$		−	551264.i		−	0.848574i
$807$			26023.9i			0.0399600i
$808$		−	462232.i		−	0.708007i
$809$	−938377.			−1.43377			−0.716886	−	0.697190i	$-0.754433\pi$
$809$	−938377.			−1.43377			−0.716886	+	0.697190i	$0.754433\pi$
$810$	434612.			0.662417
$811$			526766.i			0.800896i	0.916319	+	0.400448i	$0.131146\pi$
$811$			526766.i			0.800896i	−0.916319	+	0.400448i	$0.868854\pi$
$812$	14493.1			0.0219811
$813$		−	64038.4i		−	0.0968856i
$814$	923886.			1.39434
$815$	−23147.1			−0.0348482
$816$		−	208244.i		−	0.312746i
$817$	−62479.4	−	175596.i	−0.0936036	−	0.263069i
$818$	602499.			0.900430
$819$			293808.i			0.438022i
$820$			129042.i			0.191913i
$821$	−1.19525e6			−1.77325			−0.886626	−	0.462486i	$-0.846957\pi$
$821$	−1.19525e6			−1.77325			−0.886626	+	0.462486i	$0.846957\pi$
$822$			314628.i			0.465643i
$823$	230617.			0.340480			0.170240	−	0.985403i	$-0.445546\pi$
$823$	230617.			0.340480			0.170240	+	0.985403i	$0.445546\pi$
$824$			44331.9i			0.0652923i
$825$			630950.i			0.927016i
$826$	−155789.			−0.228338
$827$	−353042.			−0.516197			−0.258099	−	0.966119i	$-0.583096\pi$
$827$	−353042.			−0.516197			−0.258099	+	0.966119i	$0.583096\pi$
$828$	−79745.0			−0.116317
$829$		−	1.18220e6i		−	1.72021i	−0.510116	−	0.860106i	$-0.670397\pi$
$829$		−	1.18220e6i		−	1.72021i	0.510116	−	0.860106i	$-0.329603\pi$
$830$	−2.25545e6			−3.27399
$831$	−187263.			−0.271175
$832$	−611051.			−0.882736
$833$	293804.			0.423416
$834$	−109392.			−0.157273
$835$		−	2.09897e6i		−	3.01046i
$836$			27448.2i			0.0392737i
$837$			676751.i			0.966002i
$838$	−136216.			−0.193972
$839$			229327.i			0.325785i	0.986644	+	0.162892i	$0.0520823\pi$
$839$			229327.i			0.325785i	−0.986644	+	0.162892i	$0.947918\pi$
$840$	−447592.			−0.634342
$841$	681737.			0.963884
$842$	364204.			0.513712
$843$			382705.i			0.538529i
$844$		−	107177.i		−	0.150458i
$845$		−	473577.i		−	0.663250i
$846$			680283.i			0.950493i
$847$		−	137732.i		−	0.191985i
$848$	170723.			0.237411
$849$			106022.i			0.147089i
$850$			1.28340e6i			1.77634i
$851$			1.16674e6i			1.61108i
$852$	42726.0			0.0588590
$853$	736313.			1.01196			0.505981	−	0.862545i	$-0.331131\pi$
$853$	736313.			1.01196			0.505981	+	0.862545i	$0.331131\pi$
$854$		−	778301.i		−	1.06717i
$855$	292078.			0.399546
$856$		−	1.08349e6i		−	1.47869i
$857$	1.18206e6			1.60945			0.804726	−	0.593646i	$-0.202312\pi$
$857$	1.18206e6			1.60945			0.804726	+	0.593646i	$0.202312\pi$
$858$	−212936.			−0.289251
$859$			1.14109e6i			1.54645i	0.634133	+	0.773224i	$0.281357\pi$
$859$			1.14109e6i			1.54645i	−0.634133	+	0.773224i	$0.718643\pi$
$860$	74764.9	+	210123.i	0.101088	+	0.284104i
$861$	−153889.			−0.207587
$862$		−	526957.i		−	0.709186i
$863$		−	81940.4i		−	0.110021i	−0.998486	−	0.0550106i	$-0.982481\pi$
$863$		−	81940.4i		−	0.110021i	0.998486	−	0.0550106i	$-0.0175193\pi$
$864$	202376.			0.271101
$865$		−	1.05115e6i		−	1.40485i
$866$	806224.			1.07503
$867$		−	107815.i		−	0.143430i
$868$			101405.i			0.134593i
$869$	−510677.			−0.676250
$870$	111772.			0.147670
$871$	35870.3			0.0472823
$872$		−	1.17807e6i		−	1.54931i
$873$	202479.			0.265675
$874$	175325.			0.229520
$875$	1.31039e6			1.71153
$876$	−91564.3			−0.119321
$877$	−347511.			−0.451824			−0.225912	−	0.974148i	$-0.572536\pi$
$877$	−347511.			−0.451824			−0.225912	+	0.974148i	$0.572536\pi$
$878$		−	251443.i		−	0.326174i
$879$			24618.8i			0.0318632i
$880$			973553.i			1.25717i
$881$	150733.			0.194204			0.0971018	−	0.995274i	$-0.469043\pi$
$881$	150733.			0.194204			0.0971018	+	0.995274i	$0.469043\pi$
$882$		−	283423.i		−	0.364332i
$883$	−1.40226e6			−1.79849			−0.899246	−	0.437443i	$-0.855884\pi$
$883$	−1.40226e6			−1.79849			−0.899246	+	0.437443i	$0.855884\pi$
$884$	85633.9			0.109583
$885$	237540.			0.303285
$886$		−	1.17542e6i		−	1.49736i
$887$			900825.i			1.14497i	0.819916	+	0.572484i	$0.194020\pi$
$887$			900825.i			1.14497i	−0.819916	+	0.572484i	$0.805980\pi$
$888$		−	699864.i		−	0.887540i
$889$		−	834419.i		−	1.05580i
$890$			894581.i			1.12938i
$891$	−268439.			−0.338135
$892$		−	201854.i		−	0.253693i
$893$			295704.i			0.370813i
$894$		−	445848.i		−	0.557842i
$895$	2.48855e6			3.10671
$896$	−384824.			−0.479343
$897$		−	268910.i		−	0.334212i
$898$	−9821.02			−0.0121788
$899$		−	178726.i		−	0.221140i
$900$	−244776.			−0.302193
$901$	−198487.			−0.244502
$902$			403133.i			0.495490i
$903$	−250582.	+	89160.6i	−0.307308	+	0.109345i
$904$	1.05638e6			1.29266
$905$			1.11557e6i			1.36208i
$906$			175925.i			0.214325i
$907$	754265.			0.916874			0.458437	−	0.888727i	$-0.348409\pi$
$907$	754265.			0.916874			0.458437	+	0.888727i	$0.348409\pi$
$908$		−	118458.i		−	0.143679i
$909$	430440.			0.520937
$910$			772972.i			0.933429i
$911$			834583.i			1.00562i	0.864398	+	0.502809i	$0.167700\pi$
$911$			834583.i			1.00562i	−0.864398	+	0.502809i	$0.832300\pi$
$912$	−87320.8			−0.104985
$913$	1.39308e6			1.67123
$914$	−812128.			−0.972148
$915$			1.18671e6i			1.41744i
$916$	−179666.			−0.214129
$917$	−208009.			−0.247368
$918$	531724.			0.630959
$919$	−558842.			−0.661696			−0.330848	−	0.943684i	$-0.607335\pi$
$919$	−558842.			−0.661696			−0.330848	+	0.943684i	$0.607335\pi$
$920$	−1.48075e6			−1.74946
$921$		−	346570.i		−	0.408575i
$922$			233611.i			0.274809i
$923$		−	520776.i		−	0.611290i
$924$	39169.7			0.0458782
$925$			3.58131e6i			4.18560i
$926$	344750.			0.402052
$927$	−41282.8			−0.0480407
$928$	−53446.3			−0.0620614
$929$		−	911473.i		−	1.05612i	−0.849208	−	0.528059i	$-0.822920\pi$
$929$		−	911473.i		−	1.05612i	0.849208	−	0.528059i	$-0.177080\pi$
$930$			782044.i			0.904202i
$931$		−	123198.i		−	0.142136i
$932$			161213.i			0.185596i
$933$			671949.i			0.771921i
$934$	−1.05598e6			−1.21049
$935$		−	1.13187e6i		−	1.29472i
$936$		−	583042.i		−	0.665500i
$937$		−	297178.i		−	0.338484i	−0.985575	−	0.169242i	$-0.945868\pi$
$937$		−	297178.i		−	0.338484i	0.985575	−	0.169242i	$-0.0541319\pi$
$938$	33374.0			0.0379317
$939$	765735.			0.868455
$940$		−	353849.i		−	0.400463i
$941$	−44565.6			−0.0503292			−0.0251646	−	0.999683i	$-0.508011\pi$
$941$	−44565.6			−0.0503292			−0.0251646	+	0.999683i	$0.508011\pi$
$942$			43039.3i			0.0485024i
$943$	−509102.			−0.572508
$944$	256691.			0.288049
$945$		−	948927.i		−	1.06260i
$946$	233568.	+	656433.i	0.260995	+	0.733514i
$947$	−1.06777e6			−1.19064			−0.595319	−	0.803490i	$-0.702974\pi$
$947$	−1.06777e6			−1.19064			−0.595319	+	0.803490i	$0.702974\pi$
$948$			54810.7i			0.0609886i
$949$			1.11605e6i			1.23923i
$950$	538157.			0.596296
$951$		−	416202.i		−	0.460196i
$952$	562335.			0.620470
$953$		−	1.12239e6i		−	1.23583i	−0.786246	−	0.617913i	$-0.787978\pi$
$953$		−	1.12239e6i		−	1.23583i	0.786246	−	0.617913i	$-0.212022\pi$
$954$			191474.i			0.210384i
$955$	−1.17094e6			−1.28389
$956$	−47779.2			−0.0522785
$957$	−69036.2			−0.0753794
$958$		−	1.19934e6i		−	1.30681i
$959$	−705433.			−0.767041
$960$	866860.			0.940604
$961$	326988.			0.354066
$962$	−1.20864e6			−1.30601
$963$	1.00897e6			1.08799
$964$			168682.i			0.181516i
$965$		−	2.06623e6i		−	2.21883i
$966$		−	250195.i		−	0.268117i
$967$	769222.			0.822619			0.411310	−	0.911496i	$-0.365072\pi$
$967$	769222.			0.822619			0.411310	+	0.911496i	$0.365072\pi$
$968$			273319.i			0.291689i
$969$	101521.			0.108121
$970$	532697.			0.566157
$971$	1.12938e6			1.19785			0.598926	−	0.800804i	$-0.295594\pi$
$971$	1.12938e6			1.19785			0.598926	+	0.800804i	$0.295594\pi$
$972$			158281.i			0.167531i
$973$		−	245270.i		−	0.259071i
$974$			823025.i			0.867551i
$975$		−	825415.i		−	0.868287i
$976$			1.28239e6i			1.34623i
$977$	−986156.			−1.03313			−0.516567	−	0.856247i	$-0.672790\pi$
$977$	−986156.			−1.03313			−0.516567	+	0.856247i	$0.672790\pi$
$978$			7761.24i			0.00811434i
$979$		−	552540.i		−	0.576499i
$980$			147422.i			0.153501i
$981$	1.09704e6			1.13995
$982$	−436213.			−0.452351
$983$		−	777551.i		−	0.804677i	−0.915491	−	0.402339i	$-0.868197\pi$
$983$		−	777551.i		−	0.804677i	0.915491	−	0.402339i	$-0.131803\pi$
$984$	305382.			0.315394
$985$		−	872725.i		−	0.899508i
$986$	−140425.			−0.144441
$987$	421982.			0.433171
$988$		−	35908.0i		−	0.0367856i
$989$	−828987.	+	294965.i	−0.847530	+	0.301563i
$990$	−1.09188e6			−1.11405
$991$			1.84394e6i			1.87759i	0.344478	+	0.938794i	$0.388056\pi$
$991$			1.84394e6i			1.87759i	−0.344478	+	0.938794i	$0.611944\pi$
$992$		−	373953.i		−	0.380009i
$993$	−538088.			−0.545701
$994$		−	484533.i		−	0.490400i
$995$	−1.89139e6			−1.91044
$996$		−	149519.i		−	0.150722i
$997$		−	105165.i		−	0.105799i	−0.998600	−	0.0528996i	$-0.983154\pi$
$997$		−	105165.i		−	0.105799i	0.998600	−	0.0528996i	$-0.0168463\pi$
$998$	−676023.			−0.678735
$999$	1.48376e6			1.48674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.b.b.42.4	✓	12
3.2	odd	2		387.5.b.c.343.9		12
4.3	odd	2		688.5.b.d.257.6		12
43.42	odd	2	inner	43.5.b.b.42.9	yes	12
129.128	even	2		387.5.b.c.343.4		12
172.171	even	2		688.5.b.d.257.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.b.b.42.4	✓	12	1.1	even	1	trivial
43.5.b.b.42.9	yes	12	43.42	odd	2	inner
387.5.b.c.343.4		12	129.128	even	2
387.5.b.c.343.9		12	3.2	odd	2
688.5.b.d.257.6		12	4.3	odd	2
688.5.b.d.257.7		12	172.171	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.65497i q^{2} +4.18965i q^{3} +2.64117 q^{4} +45.6695i q^{5} +15.3130 q^{6} +34.3337i q^{7} -68.1330i q^{8} +63.4469 q^{9} +O(q^{10})\)	\(q-3.65497i q^{2} +4.18965i q^{3} +2.64117 q^{4} +45.6695i q^{5} +15.3130 q^{6} +34.3337i q^{7} -68.1330i q^{8} +63.4469 q^{9} +166.921 q^{10} -103.099 q^{11} +11.0656i q^{12} +134.875 q^{13} +125.489 q^{14} -191.339 q^{15} -206.765 q^{16} +240.390 q^{17} -231.897i q^{18} -100.800i q^{19} +120.621i q^{20} -143.846 q^{21} +376.825i q^{22} -475.879 q^{23} +285.453 q^{24} -1460.70 q^{25} -492.966i q^{26} +605.181i q^{27} +90.6813i q^{28} -159.825i q^{29} +699.339i q^{30} +1118.26 q^{31} -334.405i q^{32} -431.949i q^{33} -878.620i q^{34} -1568.00 q^{35} +167.574 q^{36} -2451.77i q^{37} -368.423 q^{38} +565.080i q^{39} +3111.60 q^{40} +1069.81 q^{41} +525.754i q^{42} +(1742.01 - 619.833i) q^{43} -272.303 q^{44} +2897.59i q^{45} +1739.32i q^{46} -2933.56 q^{47} -866.274i q^{48} +1222.20 q^{49} +5338.84i q^{50} +1007.15i q^{51} +356.229 q^{52} -825.685 q^{53} +2211.92 q^{54} -4708.49i q^{55} +2339.26 q^{56} +422.318 q^{57} -584.155 q^{58} -1241.46 q^{59} -505.360 q^{60} -6202.15i q^{61} -4087.22i q^{62} +2178.37i q^{63} -4530.49 q^{64} +6159.69i q^{65} -1578.76 q^{66} +265.952 q^{67} +634.912 q^{68} -1993.77i q^{69} +5731.02i q^{70} -3861.16i q^{71} -4322.82i q^{72} +8274.70i q^{73} -8961.14 q^{74} -6119.84i q^{75} -266.231i q^{76} -3539.78i q^{77} +2065.35 q^{78} +4953.26 q^{79} -9442.88i q^{80} +2603.70 q^{81} -3910.14i q^{82} -13512.1 q^{83} -379.923 q^{84} +10978.5i q^{85} +(-2265.47 - 6367.01i) q^{86} +669.609 q^{87} +7024.45i q^{88} +5359.31i q^{89} +10590.6 q^{90} +4630.77i q^{91} -1256.88 q^{92} +4685.12i q^{93} +10722.1i q^{94} +4603.51 q^{95} +1401.04 q^{96} +3191.32 q^{97} -4467.09i q^{98} -6541.32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

Introduction

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